UPDA-8 - Notes | FM Electricals

1. What is an Oscillator?

An oscillator is an electronic circuit that produces a continuous, repetitive alternating waveform without any external input signal. It converts DC power into AC power at a desired frequency.

DC Supply → [ OSCILLATOR ] → AC Output
(No input signal required)

Oscillator = Amplifier + Positive Feedback

Applications: Signal generators, radio transmitters, clocks, microprocessors, tone generators.

2. Barkhausen Criteria (Most Important)

For sustained oscillations, two conditions must be satisfied:

✅ Condition 1 (Magnitude): |Aβ| = 1
✅ Condition 2 (Phase): ∠Aβ = 0° or 360° (or multiple of 360°)

Where A = amplifier gain, β = feedback network gain, Aβ = loop gain.

┌──────────┐ ┌──────────┐
│ Amplifier│─────►│ Output │
│ A │ │ Signal │
└────▲─────┘ └──────────┘
│
└──────[ β ]────── (Feedback)
Positive Feedback: Phase shift = 0° or 360°

Exam Tip: Loop gain < 1 → oscillations die out.
Loop gain > 1 → oscillations grow (distorted).
Loop gain = 1 → sustained oscillations.

3. Classification of Oscillators

Type	Frequency Range	Network	Examples
RC Oscillators	1 Hz – 10 MHz	RC Network	RC Phase Shift, Wien Bridge
LC Oscillators	30 kHz – 30 MHz	LC Tank	Hartley, Colpitts
Crystal Oscillators	Stable (kHz-MHz)	Quartz Crystal	Pierce, Colpitts with crystal

4. RC Phase Shift Oscillator

Uses 3 RC networks in feedback path. Each RC gives 60° phase shift → total 180° from RC. Amplifier (inverting) gives another 180°.

Total phase shift = 180° + 180° = 360°

Frequency formula: f = 1 / (2πRC√6)

Gain required: Amplifier gain ≥ 29

5. Wien Bridge Oscillator

Uses Wien bridge network (series RC + parallel RC) in feedback. Non-inverting amplifier gives 0° phase shift. At resonant frequency, feedback network also gives 0°.

Frequency formula: f = 1 / (2πRC)

Gain required: Amplifier gain ≥ 3
Frequency range: 20 Hz – 20 kHz (audio range)

6. Hartley Oscillator

LC oscillator using tapped inductor (or two inductors in series) with a capacitor.

Frequency formula: f = 1 / (2π√(L_eq × C))
where L_eq = L1 + L2 + 2M

Feedback taken from inductor tap point. Frequency range: 30 kHz – 30 MHz.

7. Colpitts Oscillator

LC oscillator using tapped capacitor (two capacitors in series) with an inductor.

Frequency formula: f = 1 / (2π√(L × C_eq))
where 1/C_eq = 1/C1 + 1/C2

Feedback taken from capacitor tap point. Better frequency stability than Hartley.

8. Comparison Table

Parameter	RC Phase Shift	Wien Bridge	Hartley	Colpitts
Frequency	1Hz-10MHz	20Hz-20kHz	30kHz-30MHz	30kHz-30MHz
Feedback Network	3 RC sections	Wien bridge	Tapped inductor	Tapped capacitor
Gain Required	≥ 29	≥ 3	≥ 1	≥ 1

1. Digital Logic States

In digital electronics, only two voltage levels are allowed:

🔹 Logic "1" = HIGH = TRUE = 5V (TTL) or 3.3V (CMOS)
🔹 Logic "0" = LOW = FALSE = 0V

┌─────────────────────────────────────┐
│ Voltage 5V ──────────────────► Logic 1 (HIGH) │
│ Voltage 0V ──────────────────► Logic 0 (LOW) │
└─────────────────────────────────────┘

These two states are represented in Boolean Algebra by binary digits "1" and "0".

2. Basic Logic Gates

Gate	Symbol	Boolean Expression	Output HIGH when
AND	&	Y = A · B	ALL inputs are HIGH
OR	≥1	Y = A + B	ANY input is HIGH
NOT	○	Y = Ā	Input is LOW (inverts)
NAND	&○	Y = (A·B)̅	NOT all inputs HIGH
NOR	≥1○	Y = (A+B)̅	ALL inputs are LOW
XOR	=1	Y = A⊕B	Inputs are DIFFERENT
XNOR	=1○	Y = A⊕B̅	Inputs are SAME

3. NOR Gate Truth Table (Important for Exam)

A	B	Output (A NOR B)
0	0	1
0	1	0
1	0	0
1	1	0

NOR gate output is HIGH only when ALL inputs are LOW.

4. Boolean Algebra Laws

5. De Morgan's Theorems (Very Important)

🔥 (A · B)̅ = Ā + B̅

🔥 (A + B)̅ = Ā · B̅

De Morgan's laws are used to convert NAND/NOR gates into other gates.

Universal Gates:
• NAND gate = AND + NOT → Can make ANY gate using only NAND
• NOR gate = OR + NOT → Can make ANY gate using only NOR

6. Fan-in & Fan-out

📌 Fan-in: Number of inputs a logic gate can have.
📌 Fan-out: Number of gates that can be connected to the output of a gate.

Higher fan-out means stronger driving capability. TTL typical fan-out = 10.

┌─────┐ ┌─────┐
│Gate │─────►│Gate1│
│ │─────►│Gate2│ ← Fan-out = 3
│ │─────►│Gate3│
└─────┘ └─────┘

7. Truth Table Entries

📐 Number of entries = 2ⁿ
Where n = number of inputs.

Example: 3-input NAND gate → 2³ = 8 entries

Inputs (n)	Truth Table Entries (2ⁿ)
1	2
2	4
3	8
4	16

8. Flip-flops & FPGAs

Flip-flops are basic memory elements. Types: D, JK, SR, T.

📌 D Flip-flop: Stores data (D = Data)
📌 JK Flip-flop: Universal flip-flop (can toggle)
📌 SR Flip-flop: Set-Reset (invalid when S=R=1)
📌 T Flip-flop: Toggle flip-flop

FPGAs (Field Programmable Gate Arrays)
• Contain configurable logic blocks (CLBs)
• Most commonly use D Flip-flops for storage
• Can be reprogrammed multiple times

9. Cyclic Redundancy Check (CRC)

CRC is an error-detecting code used in digital networks.

CRC generator is based on: Modulo-2 Division

This process involves dividing input data by a fixed polynomial using binary arithmetic (XOR operations).

10. Binary Coded Decimal (BCD)

BCD represents each decimal digit (0-9) with 4 bits.

Bits required to store one BCD digit = 4 bits
Also called 8421 code.

Decimal	BCD (4-bit)
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

1. Introduction to 555 Timer

The 555 timer IC is one of the most popular and versatile integrated circuits ever made. It is used in almost every electronic circuit today for generating accurate timing pulses.

Pin Configuration (8-pin DIP):
Pin 1: Ground (GND)
Pin 2: Trigger
Pin 3: Output
Pin 4: Reset
Pin 5: Control Voltage
Pin 6: Threshold
Pin 7: Discharge
Pin 8: Supply Voltage (Vcc)

┌─────────────────────────────┐
│ ┌───┐ ┌───┐ ┌───┐ ┌───┐ │
│ │ 1 │ │ 2 │ │ 3 │ │ 4 │ │
│ └───┘ └───┘ └───┘ └───┘ │
│ 555 TIMER IC │
│ ┌───┐ ┌───┐ ┌───┐ ┌───┐ │
│ │ 8 │ │ 7 │ │ 6 │ │ 5 │ │
│ └───┘ └───┘ └───┘ └───┘ │
└─────────────────────────────┘

2. Operating Modes of 555 Timer

Mode	Description	Application
Astable	Free-running oscillator (no stable state)	Clock generator, square wave
Monostable	One-shot (one stable state)	Timer, pulse generator
Bistable	Schmitt trigger (two stable states)	Flip-flop, memory

3. Astable Multivibrator (Free-Running Oscillator)

In astable mode, the 555 timer continuously oscillates between HIGH and LOW states, producing a square wave output.

Vcc ──┬── R1 ──┬── R2 ──┬── Pin 7 (Discharge)
│ │ │
│ └────┬────┘
│ │
└──────┬───────┴──── Pin 6 (Threshold)
│
└─────────── Pin 2 (Trigger)
│
C ────────── GND

📐 Charging Time (HIGH output): T_ON = 0.69 × (R1 + R2) × C
📐 Discharging Time (LOW output): T_OFF = 0.69 × R2 × C
📐 Total Time Period: T = T_ON + T_OFF = 0.69 × (R1 + 2R2) × C
📐 Frequency: f = 1 / T = 1.44 / ((R1 + 2R2) × C)

4. Duty Cycle

Duty cycle is the percentage of time the output is HIGH in one complete cycle.

📐 Duty Cycle Formula: D% = (T_ON / T) × 100%
📐 Simplified: D% = (R1 + R2) / (R1 + 2R2) × 100%

For 50% Duty Cycle: Set R1 = R2
Then D% = (R + R) / (R + 2R) = 2R/3R = 66.7%? Wait! Actually:

Correction: For 555 timer, exact 50% duty cycle is achieved by adding a diode across R2 or using a different configuration.
But the exam formula often uses: D = R2 / (R1 + R2) for simplified calculations.

5. Solved Example (From Your PDF)

Example: 555 astable with R1 = 10kΩ, R2 = 5kΩ, C = 0.5μF

T_ON = 0.69 × (10k + 5k) × 0.5μ = 0.69 × 15k × 0.5μ = 5.175 ms
T_OFF = 0.69 × 5k × 0.5μ = 1.725 ms
T = 5.175 + 1.725 = 6.9 ms
f = 1 / 6.9ms = 144.9 Hz ≈ 143 Hz

6. Duty Cycle Solved Example (From Your PDF)

Example: Astable operating at 150 Hz with discharge time 2.5 ms. Find duty cycle.

T = 1/f = 1/150 = 6.67 ms
T_ON = T - T_OFF = 6.67 - 2.5 = 4.17 ms
Duty Cycle = T_ON / T = 4.17 / 6.67 = 62.5%

7. Number System: Binary to Decimal Conversion

The decimal number is equal to the sum of binary digits (d_n) times their power of 2 (2ⁿ).

📐 Formula: Decimal = d_n-1 × 2^n-1 + ... + d₁ × 2¹ + d₀ × 2⁰

Example: Convert 111001₂ to decimal

111001₂ = 1×2⁵ + 1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰
= 1×32 + 1×16 + 1×8 + 0×4 + 0×2 + 1×1
= 32 + 16 + 8 + 0 + 0 + 1 = 57₁₀

8. Binary to Decimal Reference Table

Binary	2ⁿ	Decimal
1	2⁰ = 1	1
10	2¹ = 2	2
100	2² = 4	4
1000	2³ = 8	8
10000	2⁴ = 16	16
100000	2⁵ = 32	32
1000000	2⁶ = 64	64
10000000	2⁷ = 128	128
100000000	2⁸ = 256	256
1000000000	2⁹ = 512	512

9. Solved Example: 294 Decimal to Binary

Example: Convert 294₁₀ to binary

294 ÷ 2 = 147 remainder 0
147 ÷ 2 = 73 remainder 1
73 ÷ 2 = 36 remainder 1
36 ÷ 2 = 18 remainder 0
18 ÷ 2 = 9 remainder 0
9 ÷ 2 = 4 remainder 1
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Read remainders from bottom to top: 100100110₂

1. Introduction to Flip-flops

A flip-flop is a basic memory element used in sequential logic circuits. It can store one bit of data (either 0 or 1).

Flip-flops are used in:
• Registers
• Counters
• Memory units
• Frequency dividers

┌─────────┐
│ Input ──┤ │
│ Clock ──┤ Flip-flop├──► Output
│ Reset ──┤ │
└─────────┘

2. Types of Flip-flops

Type	Symbol	Characteristic Equation	Application
SR Flip-flop	S,R	Q_n+1 = S + R̅Q_n	Set-Reset (invalid when S=R=1)
JK Flip-flop	J,K	Q_n+1 = JQ̅_n + K̅Q_n	Universal flip-flop (toggle when J=K=1)
D Flip-flop	D	Q_n+1 = D	Data storage (most common in FPGAs)
T Flip-flop	T	Q_n+1 = T ⊕ Q_n	Toggle (frequency division)

Exam Tip: FPGAs most commonly use D Flip-flops for data storage.

3. Flip-flop Truth Tables

📌 D Flip-flop

D	Clock	Q_n+1
0	↑	0
1	↑	1

📌 JK Flip-flop

J	K	Q_n+1
0	0	Q_n (No change)
0	1	0 (Reset)
1	0	1 (Set)
1	1	Q̅_n (Toggle)

4. FPGA (Field Programmable Gate Array)

FPGA is an integrated circuit that can be programmed after manufacturing to implement any digital logic function.

Architecture of FPGA:
• Configurable Logic Blocks (CLBs) – contain LUTs and flip-flops
• Programmable Interconnects – routing between blocks
• I/O Blocks – interface with external devices

Key Points:
• Most common flip-flop in FPGA: D Flip-flop
• Can be reprogrammed multiple times
• Used in: DSP, cryptography, embedded systems, prototyping

┌─────────────────────────────────────────┐
│ ┌───────┐ ┌───────┐ ┌───────┐ │
│ │ CLB │ │ CLB │ │ CLB │ │
│ │ + FF │ │ + FF │ │ + FF │ │
│ └───────┘ └───────┘ └───────┘ │
│ Programmable Interconnects │
│ ┌───────┐ ┌───────┐ ┌───────┐ │
│ │ CLB │ │ CLB │ │ CLB │ │
│ │ + FF │ │ + FF │ │ + FF │ │
│ └───────┘ └───────┘ └───────┘ │
└─────────────────────────────────────────┘

5. CRC (Cyclic Redundancy Check)

CRC is an error-detecting code commonly used in digital networks and storage devices.

📐 How CRC works:
1. Data is treated as a binary number
2. Divided by a fixed divisor (generator polynomial)
3. Remainder is appended as CRC code
4. Receiver performs same division and checks remainder

Exam Point:
CRC generator is based on Modulo-2 Division (using XOR operations).

Data (k bits) → [CRC Generator] → Data + CRC (n bits)
↑
Uses XOR (Modulo-2) operations

6. Measurement & Instrumentation

Measurement is the comparison between an unknown quantity and a predefined standard.

Classification of Measuring Instruments:
• Electrical Instruments
• Electronic Instruments
• Mechanical Instruments

Key Terms:
• Accuracy: Closeness to true value
• Precision: Reproducibility of measurement
• Calibration: Adjusting instrument to standard
• Error: Deviation from true value

7. Wheatstone Bridge

The Wheatstone bridge is used for precise measurement of unknown resistance.

┌─────┐
│ G │ (Galvanometer)
└──┬──┘
P ──┼────┼── Q
│ │ │ │
└───┴────┴───┘
│ │
R S
│ │
└────┬────┘
│
Battery

📐 Balance Condition: P/Q = R/S
or P × S = Q × R

Example 1: P=100Ω, Q=1000Ω, R=40Ω, find S
S = (Q/P) × R = (1000/100) × 40 = 400Ω

Example 2: P=500Ω, Q=800Ω, R=x+400, S=1000Ω, find x
500/800 = (x+400)/1000
x+400 = (500×1000)/800 = 625
x = 225Ω

8. Ammeter and Voltmeter

📌 Ammeter

Measures current. Connected in series with the circuit. Has very low resistance.

📌 Voltmeter

Measures potential difference (voltage). Connected in parallel with the circuit. Has very high resistance.

Example: Moving Coil Ammeter to Voltmeter
Given: R_m = 10Ω, I_m = 5mA = 0.005A, V = 5V

Formula: R = (V / I_m) - R_m
R = (5 / 0.005) - 10 = 1000 - 10 = 990Ω in series

Ammeter (series) ──┬── [Load] ──┬──
│ │
[Ammeter] [Voltmeter]
│ │
Parallel connection for Voltmeter

9. Calibration

Calibration is the process of comparing an instrument's measurements to a known standard.

Why calibrate?
• All electronic components drift over time
• Mechanical parts wear out
• Ensures accuracy and traceability

To make sure an instrument does not drift with time, we need to CALIBRATE it.

1. Introduction to Power System

An electric power system is a network of electrical components deployed to supply, transfer, and use electric power.

Main Components:
• Generation (Power Plants)
• Transmission (High Voltage lines)
• Distribution (Low Voltage to consumers)
• Utilization (Loads)

[Generator] → [Step-up Transformer] → [Transmission Line]
↓
[Step-down Transformer] → [Distribution] → [Consumer]

Main objective of transmission system: RELIABILITY

2. Strong vs Weak Power System

Parameter	Strong Power System	Weak Power System
Short Circuit Capability	High	Low
Sensitivity to Harmonics	Low	High

3. Transmission Line Components

The wire placed on the top of a transmission line is: Ground wire (Shield wire / Earth wire)

Purpose of Ground Wire:

Connected to steel tower body (which is earthed)
Shields phases from lightning strikes
Lightning hits ground wire instead of phase conductors
Prevents overvoltage issues

☁️ Lightning
↓
⚡ Ground Wire (Top) ← Protects phases below
─── Phase A ───
─── Phase B ───
─── Phase C ───

4. Transmission Line Parameters

Transmission line has four main parameters uniformly distributed along the line:

📌 Resistance (R) – Opposes current flow
📌 Inductance (L) – Due to magnetic field
📌 Capacitance (C) – Due to electric field
📌 Shunt Conductance (G) – Due to leakage current

Transmission Line Model: Z = R + jωL | Y = G + jωC

5. ACSR Conductor (Aluminium Conductor Steel Reinforced)

ACSR is the most popular conductor for longer transmission lines.

┌─────────────────────────────┐
│ ⚪ Steel Core (Strength) │
│ ⚪⚪⚪ Aluminium Strands │
│ ⚪⚪⚪⚪⚪ (Current carrying) │
└─────────────────────────────┘

Specification Format: Aluminium strands / Steel strands
Example: 25/7 means 25 Al strands + 7 Steel strands

Current Flow in ACSR:
• Majority of current flows through Aluminium (good conductor)
• Negligible current flows through Steel (provides strength)

Types of Conductors:
• AAC – All Aluminium Conductor
• AAAC – All Aluminium Alloy Conductor
• ACSR – Aluminium Conductor Steel Reinforced (most popular)
• ACAR – Aluminium Conductor Alloy Reinforced

6. Skin Effect

Skin effect is the tendency of alternating current (AC) to become distributed within a conductor such that the current density is largest near the surface and decreases with depth.

Conductor Cross-section:
┌─────────────────┐
│ ███████████████ │ ← High current density (surface)
│ ███░░░░░░░███ │
│ ██░░░░░░░░░██ │
│ █░░░░░░░░░░░█ │
│ ░░░░░░░░░░░░░ │ ← Low current density (center)
└─────────────────┘

Effects of Skin Effect:
• Increases effective resistance
• More pronounced at HIGH FREQUENCY
• Stranded conductors help reduce skin effect

7. Corona Effect

Corona is the ionization of air around conductors at high voltage, causing hissing noise and power loss.

📌 Factors Affecting Corona Loss:

• Larger conductor size → Lower corona loss
• Higher voltage → Higher corona loss
• Smooth surface → Lower corona loss
• Greater spacing → Lower corona loss
• Higher altitude → Higher corona loss (lower air density)
• Humid/rainy weather → Higher corona loss

📌 Effects of Corona:

• Energy loss (power wastage)
• Audible noise (hissing/crackling)
• Radio interference
• Ozone formation (conductor corrosion)

📌 Mitigation of Corona Loss:

• Use of larger conductors
• Use bundled conductors (multiple smaller conductors in parallel)
• Increase conductor spacing
• Ensure smooth/clean conductor surfaces

8. Ferranti Effect

Ferranti effect is a voltage rise at the receiving end of a long transmission line under light load or no-load conditions.

Causes:
• Capacitance of line becomes significant at low loads
• Charging current produces voltage rise due to line inductance and capacitance

Mitigation: Use of shunt reactors at the receiving end to compensate for reactive power generated by line capacitance.

9. Distribution System

Electrical system between substation and customers consists of:

📌 Feeder: Connects substation to distribution area. No tapping. Current remains same. Design based on current carrying capacity.

📌 Distributor: Conductor from which tappings are taken for consumers. Design based on voltage drop.

📌 Service Main: Small cable connecting distributor to consumer's terminals.

📌 Distribution System Configurations:

• Radial: Low reliability, low cost
• Ring Main: High reliability, higher cost
• Interconnected: Most reliable, highest cost

Distribution voltage in Qatar for residential: 230/400 V
Voltage drop limit: Should not exceed 5%

10. Earthing

Earthing is the process of transferring electrical energy directly to the earth through a low resistance wire.

For effective earthing, which mixture is preferred?
Answer: Coal-Salt mixture
• Coal (carbon) – good conductor, minimizes earth resistance
• Salt – electrolyte to form conductivity with humidity

Earthing Electrode: Rod, pipe, plate, or bundle of conductors inserted in ground vertically or horizontally.

11. Bus Schemes in Substations

Component	Symbol/Representation
Isolator	A
Current Transformer (CT)	B
Circuit Breaker	C
Isolator	D

12. Load Bus & Generator Bus

📌 Load Bus (PQ Bus): Net real and reactive power demands are specified.
📌 Generator Bus (PV Bus): Real power generation and voltage magnitude are specified.
📌 Slack Bus (Swing Bus): Only one bus. Supplies slack between scheduled generation and sum of loads + losses.

13. Control System

A control system manages, commands, directs, or regulates the behavior of other devices to achieve desired results.

📌 Open Loop Control System

Control action is independent of output. No feedback.
Example: Washing machine, toaster

📌 Closed Loop Control System

Output has effect on input quantity. Uses feedback.
Example: Air conditioner, temperature control

Open Loop: Input → [Controller] → [Process] → Output
Closed Loop: Input → [Controller] → [Process] → Output
↑________________[Feedback]___________↓

14. Transfer Function

For negative feedback: T = G / (1 + GH)
For positive feedback: T = G / (1 - GH)

Zeros: Roots of numerator (set N(s) = 0)
Poles: Roots of denominator (set D(s) = 0)

Example: G(s) = (5s-1)/(s²+5s+4)
Zero: 5s-1=0 → s = 1/5
Poles: s²+5s+4=0 → s = -1, -4

15. Protection Systems

Relay Pickup Current: = % current setting × CT secondary current
Example: 125% × 5A = 6.25 A

For symmetrical network: Neutral current = ZERO
Because I_N = I_R + I_Y + I_B and in balanced system, sum = 0

Purpose of neutral line: Return path for normal current (in unbalanced conditions)

16. Switching Sequence (Important)

📌 While OPENING a circuit:

1. Open Isolator – disconnects circuit
2. Open Circuit Breaker – breaks current flow
3. Close Earthing Switch – safely grounds circuit

📌 While CLOSING a circuit:

1. Open Earthing Switch – removes ground
2. Close Circuit Breaker – allows current flow
3. Close Isolator – secures circuit

17. Spinning Reserve & Reliability

Spinning Reserve: Generating capacity that is connected to the grid and ready to take load.

Parallel Reliability Formula:
R_total = P(a) + P(b) - P(a)×P(b)
Example: 0.92 + 0.85 - (0.92×0.85) = 0.988 ≈ 0.99

OSCILLATORS